This repository contains MATLAB-based simulations and analyses for three key homework assignments in signals & systems. Each homework explores different aspects of signal processing, system behavior, and sampling theory, using both theoretical and practical approaches.
This homework focuses on the Fourier series and its applications in signal decomposition and reconstruction. Key tasks include:
- Fourier Coefficients Calculation: Finding and analyzing the Fourier coefficients for different signals.
- Music Note Generation: Using windowing techniques to generate and compare musical tones.
- Signal Comparisons: Exploring the effects of windowing on different time-domain signals and observing the corresponding frequency-domain characteristics.
This homework explores the Laplace domain for analyzing control systems, specifically focusing on transfer functions. Major components include:
- Transfer Function Representation: Defining transfer functions using MATLAB and analyzing system dynamics.
- Pole-Zero Mapping: Plotting the poles and zeros of the transfer function to study system stability.
- Inverse Laplace Transform: Calculating and interpreting the inverse Laplace transform of complex systems.
This homework examines key concepts of digital signal processing, including sampling theory and its application to audio signals. Key tasks include:
- Sampling and Aliasing: Understanding Nyquist criteria, performing downsampling, and analyzing the effects of aliasing on sampled signals.
- Audio Resampling: Manipulating audio signals by upsampling and downsampling, and evaluating the resulting audio quality and spectral content.
- Fourier Analysis of Audio Signals: Applying FFT and visualizing the frequency spectrum of audio files.
- MATLAB R2023 or later.